MinT - Best Known (51−33, 51, s)-Nets in Base 32

Best Known (51−33, 51, s)-Nets in Base 32

(51−33, 51, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 51, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 51, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(51−33, 51, 161)-Net over F₃₂ — Digital

Digital (18, 51, 161)-net over F₃₂, using

net from sequence [i] based on digital (18, 160)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 18 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(51−33, 51, 177)-Net in Base 32 — Constructive

(18, 51, 177)-net in base 32, using

15 times m-reduction [i] based on (18, 66, 177)-net in base 32, using
- base change [i] based on digital (7, 55, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(51−33, 51, 209)-Net in Base 32

(18, 51, 209)-net in base 32, using

3 times m-reduction [i] based on (18, 54, 209)-net in base 32, using
- base change [i] based on digital (9, 45, 209)-net over F₆₄, using
  - net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
      - a curve from the manYPoints database [i]

(51−33, 51, 11077)-Net in Base 32 — Upper bound on s

There is no (18, 51, 11078)-net in base 32, because

1 times m-reduction [i] would yield (18, 50, 11078)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1809 567462 973262 313905 292392 884341 518396 676788 216649 462726 845348 417746 926972 > 32⁵⁰ [i]